The authors have collaborated for the past 40 years on a sequence of initiatives for a range of fisheries and marine ecosystems projects. These had natural mortality (M) as a common thread and have helped increase understanding of this elusive parameter. Here, we provide a reprise as well as an extension of our earlier results. Taken together, these help to develop an understanding of M of exploited fish stocks, particularly those of the North Sea. Firstly, a reprisal is given of the key findings about M due to predation by important fish stocks of the North Sea. Estimates were first produced by the ICES Multispecies Working Group using multispecies virtual population analysis (MSVPA) in combination with extensive stomach content data - collected for all four quarters and around the whole North Sea during 1981. Results from this initiative demonstrate that predation mortality (M2) represents a large portion of M for many North Sea fish species, but varies markedly both by age and by year, thus refuting the then widely adopted hypothesis that M was constant. Moreover, these variations were sufficiently large to overturn single species predictions of sustainable yield. M2 results from the 1980′s also indicated that mortality levels were related to prey size and species. The paper then reprises results from studies made by the private working group (PWG) that the authors formed to continue their collaboration. These focused first on size spectra of fish communities both by data analysis and by developing a simple trait-based model (cartoon) of the North Sea - the charmingly simple model (CSM). This modelling led to further questions about the basis of the coexistence of fish species in an ecosystem given that egg production scales approximately with asymptotic weight. This led to a plausible hypothesis that differential natural mortality rates are required that increase with the von Bertalanffy parameters of curvature K and asymptotic length L_∞, but decrease with fish length. Data from the literature supported this hypothesis, which was further refined into canonical form: M=K(L_∞/L)^1.5. However, this hypothesis is also questioned because this form might not be compatible with the predicted and observable fact that size-spectra slopes become more negative with increased general levels of fishing. Clearly, changes in size spectra should cause changes in M2. Results of new modelling work are presented where the CSM is modified to include differential natural mortality rates by K and L_∞. The results suggest that M responds both to general levels of fishing and the slope of the ensuing size spectrum. This suggests that a more general expression for predation mortality would be M2=α(F)K(L_∞^χ)(L^β(F)), where χ is likely to be close to the 1.5 value used in the canonical form. The work thus provides a likely form for M2 but by no means a universally applicable formula. It remains a hypothesis needing to be tested and perhaps calibrated against data from the sea. Such calibrations might indeed point toward a universal formula for M2.

作者在过去40年中就一系列渔业和海洋生态系统项目的一系列举措进行了合作。这些具有自然死亡率（M）作为共同点，并且有助于增加对这一难以捉摸的参数的理解。在这里，我们提供了对之前结果的补充和扩展。总之，这些有助于发展的理解中号开发的鱼类资源，特别是北海的。首先，对有关M的主要发现进行报复由于北海重要鱼类种群的捕食。ICES多物种工作组首先使用多物种虚拟种群分析（MSVPA）结合广泛的胃含量数据得出了估计值-于1981年期间针对所有四个季度和整个北海收集了该数据。该计划的结果表明，捕食死亡率（M2）在许多北海鱼类中占M的很大一部分，但随着年龄和年份而变化很大，因此驳斥了当时被广泛采用的M恒定的假设。此外，这些变化足够大，足以推翻单一物种对可持续产量的预测。M21980年代的结果还表明，死亡率与猎物的大小和种类有关。然后，本文对由私人工作组（PWG）进行的研究结果进行了重新介绍，该研究是作者为继续他们的合作而形成的。这些研究首先通过数据分析和开发简单的基于特征的北海模型（卡通），即鱼类的简单模型（CSM），着眼于鱼类群落的大小谱图。考虑到蛋的产量与渐近体重大致成比例，这种模型导致了对生态系统中鱼类共存基础的进一步质疑。这导致了一个合理的假设，即差动天然死亡率需要具有曲率贝塔朗菲参数增加ķ和渐近长度大号_∞，但随着鱼的长度而减少。从文献中数据的支持这一假设，将其进一步精炼成规范形式：中号= ķ（大号_∞/大号）^1.5。但是，这个假设也受到质疑，因为这种形式可能与预计的和可观察到的事实不符，即随着总体捕捞水平的提高，尺寸光谱的斜率变得越来越负。显然，尺寸光谱的变化应引起M2的变化。新的建模工作的结果都在CSM被修改为包括由差动自然死亡率ķ和大号_∞。结果表明，M对捕捞的总体水平和随之而来的规模谱的斜率都做出了反应。这表明，用于捕食死亡率更一般的表达将是M2 = α（˚F）ķ（大号_∞ ^χ）（大号^β（˚F）），其中χ是可能接近在规范形式中使用的1.5的值。因此，这项工作为M2提供了一种可能的形式，但绝不是一个普遍适用的公式。它仍然是一个假设，需要根据来自海洋的数据进行测试，甚至可能要进行校准。这样的校准确实可能指向M2的通用公式。